When Numbers Turn Nasty

Yesterday I joined a U3A Online talk entitled "When numbers turn nasty" - an intriguing title and I wasn't disappointed.

It was delivered over Zoom by maths educationalist and former CERN researcher Dr. Octavio Dominguez.

The number that turns nasty is

But before we found out how and why, we were taken on a tour to explain.

First of all we learnt about Mersenne numbers and Mersenne primes...

And if it is a prime number it is called a Mersenne prime. 

And if n is also a Merenne prime, then it is known as a double Mersenne prime. 

Our special number is one of only 52 known Mersenne numbers and one of only 4 double Mersenne primes that are known.

Octavio then took us on a diversion into exploring different number bases. We use the base 10 as we have 10 digits on our hands, but there is a tribe in Mexico that use Vigesiaml (base-20), using their toes for counting too.

We then focussed on binary and how it used in computers, including the concept of "Two's complement" to express signed (i.e positive and negative) numbers.

In 8 bits there are 256 possible numbers and  they cover the range -127 to +127 (+/- 2 to the power 7 -1). However computers (until relatively recently) usually store numbers in 32 bits  and the range for that is.. +/- 2 to the power 31 -1, i.e. - 2,147,483,647 to + 2,147,483,647.

Our nasty number is revealed! So why is it nasty?

Well when 32-bit computers count, when the get to 2,147,483,617 and add 1, because there isn't a 33rd bit to carry to the answer is 0!

This can cause havoc. Octavio told us about the Los Angeles Air Traffic Control system failure on 14th September 2014. The system counted in milliseconds and to avoid the problem was reset every 49 days, but on that day, the reset was forgotten.  Communicaton was lost for 3.5 hours with over 800 planes in the air. 450 flights were diverted, cancelled or delayed affecting around 30,000 people and costing millions of dollars.

A forthcoming problem is known as the Y2K38 problem. In UNIX systems time is measured in seconds from midnight on 1st January 1970 and we will get to 2,147,48,647 seconds on 19th January 2038 at 03:14:07.

The solution is to upgrade systems to 64-bits which will be safe from the rollover problem for 292 billion years.

Octavio's final example was of YouTube which counted views in 32-bits until recently, but had to upgrade to 64-bits to cope with the largest ever number of views... "Gangman Style" which, by 12 Jan 2026 had reached an astonishing  5,815, 024,507 views. 

What a great talk. Thank-you Octavio!